Answer to Question #338687 in Statistics and Probability for shimmy

Question

6. Lilian got a score of 55, which is equivalent to the 70th percentile in a mathematics test. Which of the following is NOT true?

A. 70% of the students got a score less than or equal to Lilian’s score.

B. Thirty percent of the class got scores of 55 and above.

C. If the passing mark is the first quartile, she passed the test.

D. Her score is below the 5th decile.

7. In a 50-item test, Angela got a score of 35 which is the third quartile. This means that:

A. She got the highest score.

B. Her score is higher than 25% of her classmates.

C. She surpassed 75% of her classmates.

D. Seventy-five percent of the class did not pass the test.

8. In the set of scores 14, 17, 10, 22, 19, 24, 8, 12, and 19, the median score is _______. A. 17 C. 16 B. 15 D. 13

Answer 1

6 -- To prove that the statement is incorrect, consider the value of the 5th decile and 70th decile. Decile means the score points that divide the distribution into 10 equal parts. They are often denoted by D. On the other hand, percentile is the score points which divide a distribution into one hundred equal parts, so that each part represents the data set. It is often denoted by P.

Given that Rochelle's score is in the 70th percentile and comparing decile with percentile will give: 1st decile = 10th percentile. It follows that the 5th decile = 50th percentile. But Rochelle's score is the 70th percentile which is greater than the 50th percentile or the 5th decile. Therefore, her score of 55 does not belong to the scores below the 5th decile.

7 -- third quartile = 3*1/4 = 75%

So, Angela`s score is higher than 75% of her classmates , so B is wrong

A: her score is lower than 25% of her classmates, so wrong

C: true (higher than = surpass)

D: wrong (there is not set score for passing the exam)

So, the answer is C

8 -- Rank the scores from smallest to largest:

8, 10, 12, 14, 17, 19, 19, 22, 24

And there are nine scores.

Median calculation rules: When the number of data is odd, the median is just the middle number. So, the the media scores is the fifth scores.

It is 17, answer A